
where \(\left\lbrace \alpha ,m_\mathrm {min},m_\mathrm {max},\lambda _m,\mu _m,\sigma _m,\right\rbrace  \in \Lambda \)  are the population hyperparameters defining this distribution.
This model includes two components.
The first is a truncated power-law distribution with spectral index \(\alpha \)  and a maximum mass of \(m_\mathrm {max}\)  (enforced by the Heaviside step function \(\Theta \) ).
The second is a Gaussian component with mean \(\mu _m\)  and standard deviation \(\sigma _m\) .
The parameter \(\lambda _m\)  is a mixing fraction, which determines the fraction of binaries associated with either component.
The factors \(\mathcal {A}\)  and \(\mathcal {B}\)  are normalization constants that depend on the other population hyperparameters.
This mass distribution is chosen to enforce the expected cutoff in the black hole mass spectrum from PISNe [1]}, [2]}, [3]}, with the Gaussian capturing a buildup from PPSNe [4]}, [5]}, [6]}.
